This construction is not unique to Eastern Slavic languages, for example, Irish also uses it (they don't have the verb "to have" at all). Basically a construction with "У мене є" translates to English as "(There's) [something] at me"
Can all instances of "У _ є _" that indicate possession be replaced by the verb "мати", and would it be natural?
Something like that: У мене є = Я маю, У нього є = Він має, У них є = Вони мають and so on. Both forms are equally common
There are some people in Ukraine who insist on using only "Я маю". They argue that this is the traditional form and "У мене є" is just a calque from Russian. Nevertheless, there are a lot of examples of "У мене є" in our classic literature.
Who is right? I don't know. But both variants are popular
I'm not a Ukrainian, but generally in Slavic languages "У" (U) means "at" (someone's place) or "on" (like in "I have no money on me"). I don't know why Eastern Slavic languages use this particular expression, but that's the logical link.
How can you tell which nouns are neutral if it is an object? If it is a person or animal, feminine and masculin is easily distinguished. But if it is an object, I can't tell.
In most cases Masculine nouns end in a consonant, Feminine nouns have endings -а and –я, Neuter nouns have endings -о and –е.
And it is also acceptable for objects: телефон - masculine, фото - neuter.
You should use "у" before consonant in the beginning of sentence. But actually if you use "в" in this case nobody pay attention for it.
They don't give the word "telephone" as an option; just phone and cell to make tbe word cellphone....